Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computation of isomorphism classes of $p$-groups
HTML articles powered by AMS MathViewer

by Rodney James and John Cannon PDF
Math. Comp. 23 (1969), 135-140 Request permission


$p$-groups may be classified by splitting the groups up into classes having the same commutator relations (isoclinism classes) and then determining the nonisomorphic groups in each class. This paper reduces the problem of determining the isomorphism classes to that of finding the equivalence classes of a set of matrices under some equivalence relation. A computer is used to find the equivalence classes for the first few values of $p$, and these are then used as a guide for finding the solution for general $p$.
  • N. Blackburn, On a special class of $p$-groups, Acta Math. 100 (1958), 45–92. MR 102558, DOI 10.1007/BF02559602
  • T. Easterfield, A Classification of Groups of Order ${p^6}$, Ph.D. Dissertation, Cambridge Univ., Cambridge, 1940.
  • Marshall Hall Jr. and James K. Senior, The groups of order $2^{n}\,(n\leq 6)$, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0168631
  • P. Hall, The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141. MR 3389, DOI 10.1515/crll.1940.182.130
  • R. James, The Groups of Order ${p^6}(p \geqq 3)$, Ph.D. Thesis, Univ. of Sydney, 1968. O. Schreier, β€œΓœber die Erweiterung von Gruppen. II,” Abh. Math. Sem. Univ. Hamburg, v. 4, 1926, pp. 321–346.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 20.40
  • Retrieve articles in all journals with MSC: 20.40
Additional Information
  • © Copyright 1969 American Mathematical Society
  • Journal: Math. Comp. 23 (1969), 135-140
  • MSC: Primary 20.40
  • DOI:
  • MathSciNet review: 0238953